如图,在梯形ABCD中,已知AD∥BC,AB=CD,延长线段CB到E,使BE=AD,连接AE、AC. (1)求证:△ABE≌△CDA; (2)若∠DAC=40°,求∠EAC的度数.

问题描述:

如图,在梯形ABCD中,已知AD∥BC,AB=CD,延长线段CB到E,使BE=AD,连接AE、AC.

(1)求证:△ABE≌△CDA;
(2)若∠DAC=40°,求∠EAC的度数.

(1)证明:在梯形ABCD中,∵AD∥BC,AB=CD,∴∠ABE=∠BAD,∠BAD=∠CDA,∴∠ABE=∠CDA在△ABE和△CDA中,AB=CD∠ABE=∠BE=DACDA,∴△ABE≌△CDA.(2)由(1)得:∠AEB=∠CAD,AE=AC,∴∠AEB=∠ACE,∵∠DA...